Finite Gröbner basis algebra with unsolvable nilpotency problem and zero divisors problem

2016/06/05 by Ivanov-Pogodaev, Ilya, Malev, Sergey
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1606.01566

Abstract

This work presents a sample constructions of two algebras both with the ideal of relations defined by a finite Gröbner basis. For the first algebra the question whether a given element is nilpotent is algorithmically unsolvable, for the second one the question whether a given element is a zero divisor is algorithmically unsolvable. This gives a negative answer to questions raised by Latyshev.

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